Question

If 5th term of an ap is zero .prove that its 38th term is triple of its 16th term

Answer 1

5th term of the AP = 0

a + ( 5 -1 ) d =0

a + 4d = 0

a = - 4d               ------: ( 1 )

Now,

38th term of the AP = a + ( 38 - 1 )d

                                  = a + 37d

From ( 1 ), a = - 4d

                                  = - 4d + 37d

                                  = 33d    

16th term of the AP = a + ( 16 - 1 )d

                                  = a + 15d

From ( 1 ) , a = - 4d

                                  = - 4d + 15d

                                  = 11d

Then,

16th term of the AP = 11d

38th term of the AP = 33d

                                   = 3 × 11d

38th term of the AP = 3 × 16th term of the AP

Hence, proved that if 5th term of an ap is zero , then its 38th term is triple of its 16th term

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